Stability estimates on general scalar balance laws. (English) Zbl 1160.35473
Summary: Consider the general scalar balance law in \(N\) space dimensions \(\partial _tu+\text{Div} f(t,x,u)=F(t,x,u)\). Under suitable assumptions on \(f\) and \(F\), we provide bounds on the total variation of the solution. Based on this first result, we establish estimates on the dependence of the solutions from \(f\) and \(F\). In the more particular cases considered in the literature, the present estimate reduces to the known ones.
MSC:
| 35L65 | Hyperbolic conservation laws |
| 35B35 | Stability in context of PDEs |
| 35B45 | A priori estimates in context of PDEs |
Keywords:
bounds on the total variationReferences:
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